This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376305 #11 Sep 21 2024 22:57:01 %S A376305 1,2,1,3,1,2,1,2,1,3,1,2,1,2,1,2,1,3,1,4,2,1,2,1,3,1,2,1,2,1,3,1,3,1, %T A376305 2,1,2,1,2,4,1,2,1,2,1,2,1,3,1,3,1,4,2,1,2,1,3,1,2,1,2,1,3,2,3,1,2,1, %U A376305 2,1,3,1,3,1,2,1,2,1,3,1,2,1,2,1,2,1,3 %N A376305 Run-compression of the sequence of first differences of squarefree numbers. %C A376305 We define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, run-compression removes all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1). %e A376305 The sequence of squarefree numbers (A005117) is: %e A376305 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ... %e A376305 The sequence of first differences (A076259) of squarefree numbers is: %e A376305 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ... %e A376305 The run-compression is A376305 (this sequence). %t A376305 First/@Split[Differences[Select[Range[100],SquareFreeQ]]] %Y A376305 This is the run-compression of first differences of A005117. %Y A376305 For prime instead of squarefree numbers we have A037201, halved A373947. %Y A376305 Before compressing we had A076259, ones A375927. %Y A376305 For run-lengths instead of compression we have A376306. %Y A376305 For run-sums instead of compression we have A376307. %Y A376305 For prime-powers instead of squarefree numbers we have A376308. %Y A376305 For positions of first appearances instead of compression we have A376311. %Y A376305 The version for nonsquarefree numbers is A376312. %Y A376305 Positions of 1's are A376342. %Y A376305 A000040 lists the prime numbers, differences A001223. %Y A376305 A000961 and A246655 list prime-powers, differences A057820. %Y A376305 A003242 counts compressed or anti-run compositions, ranks A333489. %Y A376305 A005117 lists squarefree numbers, differences A076259. %Y A376305 A013929 lists nonsquarefree numbers, differences A078147. %Y A376305 A116861 counts partitions by compressed sum, by compressed length A116608. %Y A376305 A274174 counts contiguous compositions, ranks A374249. %Y A376305 Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A274174, A373197, A373198, A375707, A375708. %K A376305 nonn %O A376305 1,2 %A A376305 _Gus Wiseman_, Sep 20 2024